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Chapter 6 AM: Motion in One Degree of Freedom $8.03
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Chapter 6 AM: Motion in One Degree of Freedom

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The main objective of this course is to introduce students of physics to the 'modern' formalism of classical (or Newtonian) mechanics, especially Lagrangian and Hamiltonian mechanics. An important part of the course will focus on introducing the variational methods and principles in mechanics, or ...

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  • January 8, 2023
  • 32
  • 2020/2021
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LinearMotion
Jawad Cheayto

Def A linearmotion is a motion with onedegree of Audio 1

freedom
Motion

along
In case of a system having onedegree of GC 9
freedom evolving in a conservative
field with
potential
V91
We have only I Gncoordinate
As
L a g 92
1 V19

Specialcase
Audio2
CartesianCoordinates x rectilinear motion
g
Motion
mid Ux along
St.line


o
L

mi day O
f
mis du
dx
mix du
day I
at

, da Izmit da


mi't4 0
da
f
MIYU East

milk E Ux i
f2ExD
m
take t



aedm.t
dt
sfmdt f.ua

amfttk.FI u
s2mft

fcd.uf. tqfMzfed
futB Audio3
Motion is possible
only
when E USO

, Audio4 5
Motion occurs the
in region
where Utx LE

Example Assumethat ULI is givenby
thefollowing curve

U
I I TH E est
A B C D f



H
11111111111 il11Him
g 43 Xy
classically
these
areforbidden regions


IF motion ispossiple in Regions I I 4 HI
The points ABC D and F are solution to the equation VIX E
In region II
the domain of motion is unlimited

and the particle can travel infinity away Audio 6

, Two bodies problem
Audio't
considerthe sun Earth
system
as isolated
E


S Morag


Consider an isolated
system composed of
two masses magma having a force of
interaction


II.gadU
In a certain inertial reference
z
Audios
frame themotion ofthe CM
rectilinear
Cofmstmalis Miri.aqq
uniform motion a
pus R
ma
O pia

System Goof Y
Inoconstraints

K
x

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